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# Word problem

we have a house on a ten acre plot and we are selling the house with 4 acres. The assessor or treasurer tells us that the house is worth 50,000 and the land 20 thousand. The total tax is 1,000. How much of the tax is attributable to the 6 acres we are selling.

### 3 Answers by Expert Tutors

David W. | Experienced ProfExperienced Prof
4.4 4.4 (47 lesson ratings) (47)
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[important note:  Ill approach this as though you meant, "How much of the tax is attributable to the 6 acres we are not selling?" ]

Tax is computed on the assessed value of the property (not the market value).  The problem gives the total value as:  \$50,000 + \$20,000 = \$70,000.  The tax on that total is \$1000, or 1/70 the value.

Assuming that the land with the house is worth the same amount as the rest of the land, the amount of the land not being sold is 6/10 of \$20,000 = \$12,000.  At the 1/70 tax rate that means the tax should be:
(1/70) * \$12,000 = \$171.43

This is a proportion in math:
The total tax is to the total value as the remaining land tax is to the remaining land value
\$1000 / (\$50000 + \$20000)   =            x                           /  [ (6/10)(\$20000) ]
1000/70000 = x /12000
1/70 = x / 12000
12000 / 70 = x
\$171.43 = x
Mark M. | Mathematics Teacher - NCLB Highly QualifiedMathematics Teacher - NCLB Highly Qualif...
4.9 4.9 (188 lesson ratings) (188)
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Without making any unfounded assumptions as to the comparative value of the house and the land, the value of the land accounts to 2/7 of the assessment.

(2/7) · \$1000 ≈ \$285.71

The tax on the sold land is

(6/10)(\$285.71) ≈ \$171.43
Alexei M. | Patient, Knowledgeable Arts and Science TutorPatient, Knowledgeable Arts and Science ...
4.6 4.6 (7 lesson ratings) (7)
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We are not told anything bout the 6 acre house or the land. A simple proportion should do when you calculate that
4 acre/\$1000=6 acre/X
x=\$1500.00